Evolution, Randomness, and Hashkafa.--By Dr. Lee Spetner .
http://members.xoom.com/torahscience/evol1.htm
Based upon comments by those who have read his book, this
seems something like an extended abstract for the book.
Here I will give some general comments based upon the above.
It seems that Spetner's definition of information has to
do with specificity. What Spetner means by this term
becomes clear after looking at his examples. In the
WWW article mentioned above there is a section "No
Mutations Are Known That Add Information". In this
section he gives two examples. The first is "...a single
nucleotide substitution in the DNA of a bacterium giving
it immunity to streptomycin." Using an intuitive notion
of information it seems rather obvious that this new
immunity should be considered an increase in information.
Spetner argues that this actually represents a decrease
in information. His argument is interesting in that it is
counter-intuitive.
Here I'll try to summarize the argument trying to avoid
too many details. The reason the information decreases
is that the immunity is attained due to a decrease in
specificity. How so? Well, the drug works because the
mycin molecule is able to fit snugly into a matching site
on the bacterial ribosome, "like a key fitting into a lock".
The mutation causes a sufficient change in "shape" of the
matching site so that the key no longer fits. This is what
is meant then by the loss of specificity which is presumably
then a loss in information. Spetner emphasizes that there
are many mutations which result in this loss of specificity.
For example:
% "As you can see from Figure 2, the change could be in
% any one of several places on the matching site to make
% the bacterium resistant. Any one of several changes in
% the attachment site on the ribosomal protein is enough to
% spoil its match with the mycin. That means that a change
% in any one of several DNA nucleotides in the corresponding
% gene can grant resistance." -- Spetner
the number of ways that something can be done. The fewer
the ways, the greater the specificity. Or, we can think of
specificity as being the amount of precision required in
describing the structure of something. This makes sense it
seems for specificity, but does specificity correlate with
information?
As a further illustration, let's take yet another look at Yockey's
calculations for cytochrome c. This is the one where there turns
out to be umptitygazillion functionally equivalent cytochrome c
molecules. Here I'll present the results in a somewhat different
fashion to better illustrate the relation between this huge number,
the information content and the specificity.
The idea of functional equivalence is that not every position of
the sequence has to be specified uniquely, i.e. more than one
amino acid can be placed at that site and retain functionality.
Knowledge of this fact decreases the uncertainty and thus the
information content. Taking this into account requires a lot of
tedious calculations. Skipping those :), the final result is that
the information content of cytochrome c is about 2.82 bits per
symbol. If we let the per symbol information be H then the
total number M of functionally equivalent cytochrome c molecules
is found from
M = [2^H]^N
where N is the number of characters in the sequence. N = 110 for
cytochrome c so [2^2.82]^110 =~ 2*10^93.
Now, with such an enormously huge number of possible cytochrome c
molecules it might seem that the specificity for cytochrome c must
be pretty small. But, for specificity one is concerned not just with
the number of ways of doing something but rather with the ways of
doing it right relative to the total number of ways of doing it. The
number of possible amino acid sequences of length 110 is about
10^137, so the ratio of getting it right to total ways of doing it is
about 10^-44. Thus, we must conclude that cytochrome c is highly
specified wrt its function.
Now comes something that seems counter-intuitive, so beforehand
I better state my standard disclaimer, i.e. that I'm not an expert
in this subject, it's just a hobby :). I know that there are a few
individuals here who know a great deal more about information
theory than I do, so if I'm missing something please straighten
me out.
Anyway, suppose that the information content were slightly
higher, say H = 2.90 instead of 2.82. In this case we have
M = [2^2.90]^110 =~ 1*10^96 and the ratio from which we
infer specificity is [10^96]/[10^137] = 10^-41. This clearly
shows that as the information content (as used by Yockey)
increases, the specificity decreases.
The reason for this is that when Yockey says something like
"310 bits {2.82*110} of information are needed to specify
cytochrome c" he means 310 bits are needed to know which
cytochrome c from the ensemble of 2*10^93 possible cytochrome
c molecules. Now, a natural question is whether this is what is
typically meant when one is talking about information stored
in a genome. The implications wrt to Spetner's use of the
term specificity become obvious when one considers the case
when a sequence is unique, completely specified. This is the
case where specificity a la Spetner is maximum. But, if the
sequence is unique then there is only one message in the
ensemble, there is no uncertainty, and the information content
is therefore zero.
OK, let's leave this aside for the moment and address the main
point I had in mind when bringing up Yockey. When Yockey is
discussing information content of cytochrome c the information
content is wrt the normal biological function of the molecule.
Is this what Spetner is talking about when he says a point
mutation results in a loss in information? Not unless one
considers dying when exposed to streptomycin a biological
function of the bacterial ribosome.
So, if someone wants to insist that the mutation results in a
loss in information then let them at least be specific about
what information is being lost. Let them say "the mutation
resulted in the loss of the information required to die when
exposed to streptomycin." Stated this way, the observation
can hardly be considered an objection to evolution ;-).
Brian Harper
Associate Professor
Applied Mechanics
The Ohio State University
"It appears to me that this author is asking
much less than what you are refusing to answer"
-- Galileo (as Simplicio in _The Dialogue_)